High-density volumetric super-resolution microscopy

Volumetric super-resolution microscopy typically encodes the 3D position of single-molecule fluorescence into a 2D image by changing the shape of the point spread function (PSF) as a function of depth. However, the resulting large and complex PSF spatial footprints reduce biological throughput and applicability by requiring lower labeling densities to avoid overlapping fluorescent signals. We quantitatively compare the density dependence of single-molecule light field microscopy (SMLFM) to other 3D PSFs (astigmatism, double helix and tetrapod) showing that SMLFM enables an order-of-magnitude speed improvement compared to the double helix PSF by resolving overlapping emitters through parallax. We demonstrate this optical robustness experimentally with high accuracy ( > 99.2 ± 0.1%, 0.1 locs μm−2) and sensitivity ( > 86.6 ± 0.9%, 0.1 locs μm−2) through whole-cell (scan-free) imaging and tracking of single membrane proteins in live primary B cells. We also exemplify high-density volumetric imaging (0.15 locs μm−2) in dense cytosolic tubulin datasets.

The optical implementation is the poorer side of the article.For example, if simple calculations are carried out, a theoretical value of N=2.4 is obtained for the described optical configuration.However, the authors show experimental images with N=3 .But this should not be possible, unless the microlenses were projected not at the stop aperture, but very far from that position.In such a case, more than 2.4 microlenses could receive light from the sample, but with very strong vignetting (as can be seen in the Supplementary Movies 2, 3 and 4).Another problem that I detect in the images is the strong overlap between the views (this is very apparent in images 426778_0_data_set_7579143_rts8kj.tif).This should never happen and could be avoided by inserting the proper field stop.
All these optical mismatches cause the system to provide much poorer perspective views than the Fourier lightfield can provide.Therefore, the results in single-molecule tracking could be much more impressive than those reported here.Therefore, I encourage the authors to work further on the optical implementation, which will allow them to provide much more useful results to the research community.
3.-The reconstruction algorithms do not seem to be new, but rather the same (or slightly modified) as others previously reported by the same authors.
In summary, the theoretical comparison between different single-molecule tracking techniques is interesting and rigorous, but I don't think it provides enough new science to merit publication in Nature Communications.On the other hand, the implementation of "high-density volumetric super-resolution microscopy" does not seem to contribute new science and is very poor since the systems are not optimally designed and implemented.
Based on all these facts and ideas, I am afraid I cannot recommend acceptance of this article.
Reviewer #2 (Remarks to the Author) The manuscript "High-density volumetric super-resolution microscopy" by Daly et al. focuses on the quantification of accessible emitter densities in single-molecule light field microscopy (SMLFM).In SMLFM, an array of micro lenses (MLA) is placed in the Fourier plane (conjugated back-focal plane) creating a pattern of PSFs that are then recorded via a camera and analysed using standard (for PSF localisation) and custom (for connecting the localisations from the different areas) software.The work is a logical extension of the author's previous work (Sims et al., reference 22), in which the concept and the ability to image an impressive z-range of 8 µm had been demonstrated.Here, the authors used a customised MLA with a hexagonal arrangement improving the usable area on the camera.In addition to the comparison with other methodologies enabling 3D resolution in SMLM, the authors further demonstrate successful single-particle tracking over an extended biological object (B cell receptors).The manuscript is generally well written but could, in my opinion, be considerably sharpened to provide necessary information and additional clarity to the reader.As of now, I feel that some of the comparisons with other methods are not carried out as stringent as I would have liked to see them.Overall, I still consider the manuscript a very valuable addition to the field and I hope that the authors will find the following points useful to improve the manuscript.
Major points -Figure 1 a/b): If I am not mistaken, the work uses a 4f arrangement of lenses as shown in one of the SI figures and not the arrangement shown here.I would suggest to merge the SI figure and the current Figure 1.-Figure 1/2: I find it rather confusing to see different pixel sizes for different modalities in, apparently, the same field of views (in terms of constant area?).Is the reason for this a different effective magnification of the optical system?This choice makes comparing achievable emitter densities on a given camera frame area (!) rather difficult.(see also next point) -Figure 2a: If the FoV stays the same (10x10µm), the different binning would mean that even in a standard configuration 4x less molecules could be placed when a larger pixel size is used, correct?Is Fig 2b correcting/normalising for the different magnification?It is surprising to see Light Field doing so well compared to Standard with the 4x lower number of pixels.(The focal length of both Fourier lens or MLA was given as 175mm so I would not have expected any changes in magnification, correct?) -Figure 2b: The most widely used quality of imaging metric is the Jaccard index defined as JI = TP / TP + FP + FN (see, e.g.reference 6 and 12).Is there a particular reason to use precision (PPV) and sensitivity instead?If not, the authors might considering replacing sensitivity and precision with the Jaccard index to increase the overall readability of the entire manuscript.
-Figure 2: The authors cite the work on Tetrapods by the Shechtman lab (Nehme et al, reference 6), but somewhat hide the fact that the particular publication explicitly discusses how largely overlapping PSFs can be retrieved by their deep learning approach (DeepSTORM3D).For a truly fair comparison with the state of the art, tetrapods should be analysed with the best possible software, especially keeping it might that the authors here, also use customised software to map the localisations.It might well be, that DeepSTORM3D/DECODE on tetrapods is comparable in the achievable density without taking much away from the novelty and simplicity of the approach demonstrated here with the MLA.-Figure 5: One thing that is not yet discussed is the "real-estate" on the camera.As the camera sensor is now covering multiple field of views when using MLA, the achievable "throughput" is lower than in standard configuration.Could the authors comment on that?-line 129. photon numbers: 1000 photons (and not counts, I assume) per frame for a fluorescent protein is very optimistic number to get for longer than one frame (see also next point).Also, can the authors define what they mean by "next-generation fluorescent probe"?-Figure 4: Tracking over such a large sample is impressive!With an average track length of 12 localisations using a very good probe, SMLFM seems rather photon hungry.So how does the approach fares with photon numbers of well below 1000 photons per localisation?-No comments were made on the availability of the customised Matlab scripts for combining the localisation data from the different FoVs.Ideally, the software will be made available on Github (or is already).
-No comments were made on the availability of the customised MLA.Can the MLA be bought from CAIRN?Is there an estimated sales price?
Minor points -both abbreviation are present in the abstract: SMLFM and SMFLM.Please check for typos.
-Non of the figures of the SI were numbered in the final compiled PDF that I got.( I later saw that the SI itself shows everything correctly) -Figure 1a: unit for density is missing -line 125: 20x20µm mentioned here, figure shows 10x10µm, so 0.5 locs per 10x10 I assume?-line 220-222: phrasing.I somewhat doubt that the division of background photons has a larger effect than adding up the camera noise contributions from adding up seven field of views.Please comment.
-I might have missed that, how was the FSC calculated (software)?3D, as in shell, correct?-line 565: What do the authors mean by creating an evanescence wave?If I am not mistaken, TIRF would require an oil immersion objective with an NA of >1.4.
-I am surprised to see the mentioning of #1 cover slips.In most cases, the objectives are designed for #1.5 to minimise aberrations etc. Worth checking.
-line 575 unit missing -how "easy" is it to adapt the software/noise model for sCMOS rather than emCCD?
Reviewer #3 (Remarks to the Author) Daly et al present a new approach to volumetric SMLM imaging, splitting the light according to its position in the back focal plane and thereby forming multiple images, each taken at a different angle.This is a potentially very useful new approach; while many solutions have been suggested to the challenge of how to discriminate axial position, astigmatism is still the most commonly used method despite its limitations (limited z depth in a single slice, degradation of x or y precision).In particular, the authors demonstrate that their method allows use of substantially higher excitation densities than can typically be used in 3D imaging.Overall this paper represents an important and interesting new technique that could help uncover exciting new biology.However, I have some comments that I would like to be addressed.
While the acquired data is impressive the imaging of B cell receptors have a key limitation.Given the size of the cell and the number of molecules localised, I estimate that if the molecules are evenly spaced they are around 70nm apart.They are of course not evenly distributed, but it illustrates that the resolution is likely to be limited in at least some areas by the sampling rather than localisation precision (a common problem when imaging with dSTORM in thick samples).The acquired density of molecules can be limited if only a small amount of the labelled molecule is present, or by the labelling efficiency, the dSTORM blinking degrading, or the acquisition time: the authors should comment on what limited the reconstructed density in this case.
I generally think it is important to benchmark against a known structure in an experiment when presenting new techniques.However in this case, as the focus is on accurate recall at high density rather than resolution per se, I think that the evaluation is satisfactory without additional experiments.
Minor concerns 1) With regard to the double helix point spread function, a brief mention of the tradeoff between PSF size and DoF for this particular technique would be helpful.2) "this work will focus on techniques that yield sub-diffraction axial precision over extended axial ranges" -it needs to be clarified that the authors mean single shot techniques, stitching together multiple reconstructed planes is a standard approach to this problem.3) In Figure 3a the standard and astigmatic curves look flat but I think would in fact vary.Could these curves also be shown with the vertical axis expanded so this can be seen?4) In Figure 2 I found the labels giving the DoF in panel B confusing, I think the figure would be clearer with them removed.5) In Figure S5 the dark grey and black lines cannot be clearly distinguished, the lines should either be colour or separated into individual graphs.6) I don't think the PPV/sensitivity values are particularly helpful for the experimental data since this is from simulation.The expected high performance of the technique has been made clear in the part of the paper covering the simulations.7) The FSC measurement seems lower than I would expect (while the figure may seem quite high for SMLM accurate FSC measurements tend to come out substantially higher than other resolution metrics), probably due to the calculation not taking into account multiple localisations of the same flurophore.This is a known challenge in dSTORM which can bias measurements, and if it has not been corrected for then a note (e.g.no correction for fluorophore reappearance) should clarify that.8) In the image of the microtubles the upper part of the super-resolution image appears substantially degraded compared to the lower part.Why is this?Was it due to issues keeping the excitation density low in this area?Or was this at the edge of the imaging area and this caused a degradation in quality?
General remarks to reviewers are in blue; changes to the manuscript are in italicised blue.

Reviewer #1 (Remarks to the Author) (Also see attached document)
The document can be divided into two different, almost independent parts.In the first part, the paper reports a very interesting study comparing the performances of different microscopy techniques when used for the single-molecule tracking task.
The study is carried out computationally.Its implementation is rigorous, and its results can be of great help to researchers interested in tracking a single molecule in 3D.However, by itself, this part does not merit publication in Nature Communications, as it does not contribute new science.
We thank the reviewer for their time and comments recognising the relevance of our work to help researchers.
More serious are my concerns about the second part of the article in which, as the authors themselves state, they report "the first hexagonal SMLFM platform that enables 3D-SMLM in an axial range of 8 μm".From my point of view, this is the poorest part of the job, for the following reasons: 1.I don't see anything new here.Hexagonal microlenses are widely used in Fourier light field (see articles published by the research groups writing references [23] and [24] of the manuscript).In fact, the system configuration in this article is quite similar, apart from the hexagonal geometry, to the one reported by the same authors in their OPTICA article.
We appreciate the comment and have amended the text to be clearer and avoid misunderstanding.
The key conceptual advance in our paper was a high density 3D super-resolution technique that implements the principles of Fourier light field microscopy, we achieved this with a (yet unpublished) hexagonal MLA.This novel implementation required the development of a bespoke MLA and a new computational approach to light field fitting (available here: https://github.com/TheLeeLab/hexSMLFM).
We have therefore amended the text as follows to clarify: "We report the first implementation of single-snapshot 3D super-resolution imaging over an 8 µm DoF using a hexagonal MLA." The proposed optical setup is neither well designed nor well implemented.On the one hand, the use of very large focal lengths (both for the Fourier lens and for the microlenses) results in a very long add-on (I calculate 525 mm) and a very small FoV (40 um).Surely other authors (or even the same authors) have proposed better designs.

RESPONSE TO REVIEWERS' COMMENTS
We apologise for the confusion here, but we politely disagree with the comments about design.
As volumetric super-resolution experiments require much higher laser fluence than, for example, diffraction limited FLFM, a FoV of 40 µm is typical (see https://doi.org/10.1002/anie.202206919 or https://doi.org/10.1038/s41467-017-02563-4). We would argue that a 'fine-tuned optical optimization' is not a major goal of the manuscript, which is to demonstrate and quantify high-density 3D-SMLM.Regarding the physical size, this is in line with other single-molecule fluorescence microscopes.We used long focal length lenses to minimise field curvature and not for spatial requirements.
The optical implementation is the poorer side of the article.For example, if simple calculations are carried out, a theoretical value of N=2.4 is obtained for the described optical configuration.
However, the authors show experimental images with N=3 .But this should not be possible, unless the microlenses were projected not at the stop aperture, but very far from that position.
In such a case, more than 2.4 microlenses could receive light from the sample, but with very strong vignetting (as can be seen in the Supplementary Movies 2, 3 and 4).
We agree that the microscope platform could be better characterised, so we have populated the Supplementary Information with optical quantities and characterising figures.The updated Table S1 details the physical parameters of the microscope platform in this study.The bespoke MLA was designed to fit the BFP, and to illustrate that all 7 lenses of the MLA are fully illuminated (giving N = 3) we used a camera to locate and image the back focal plane, shown in Fig. S3.The BFP diameter was measured at 7.3 mm, which taken with the MLA pitch (which is equal to double the inradius) at 2.39 mm, gives N = 3.05.N = diameter of BFP / pitch = 7.4 mm / 2.39 mm = 3.10 (theoretically calculated) N = 7.3 mm / 2.39 mm = 3.05 (experimentally measured) Another problem that I detect in the images is the strong overlap between the views (this is very apparent in images 426778_0_data_set_7579143_rts8kj.tif).This should never happen and could be avoided by inserting the proper field stop.
While we agree that full dilation of the iris at the focal plane combined with highly inclined illumination leads to non-uniform background signal, this has no effect on the resulting localisation precision.This is illustrated by the resolution of individual microtubules in Fig 5 , where the super-resolved images are consistent with the state of the art in the field (see https://doi.org/10.1002/cphc.201300880 and https://doi.org/10.1017/S1431927620018620).
All these optical mismatches cause the system to provide much poorer perspective views than the Fourier lightfield can provide.Therefore, the results in single-molecule tracking could be much more impressive than those reported here.Therefore, I encourage the authors to work further on the optical implementation, which will allow them to provide much more useful results to the research community.
To avoid ambiguity, we have significantly expanded the optical characterisation of the SMLFM platform in the SI, in particular by adding Fig. S11, which is a precision curve at specific photon fluences.The curve illustrates near isotropic (xyz) localisation precision below 30 nm for an output of 2,500 photons per molecule, improving to <20 nm for 4,000 photons--typical for a dye like AF647.Altogether, this illustrates the strong resolvability of SMLFM at high density with exceptional sub-diffraction resolution.
2. The reconstruction algorithms do not seem to be new, but rather the same (or slightly modified) as others previously reported by the same authors.
The reviewer raises an important point that further development is needed in the optimal analysis pipeline, but we reserve this for a future, more focussed, study.
We have however made all code available for the first time to enable others to implement SMLFM in their work; see both Zenodo (https://doi.org/10.5281/zenodo.8190164)and GitHub (https://github.com/TheLeeLab/hexSMLFM).The fitting code had to be adapted to facilitate both hexagonal and square arrays in this work for futureproofing.
In summary, the theoretical comparison between different single-molecule tracking techniques is interesting and rigorous, but I don't think it provides enough new science to merit publication in Nature Communications.On the other hand, the implementation of "high-density volumetric super-resolution microscopy" does not seem to contribute new science and is very poor since the systems are not optimally designed and implemented.
We thank the reviewer for their valuable comments, and we appreciate the recognition of the rigorous nature of the PSF comparisons.
The key conceptual advancement of the manuscript is 'High-density volumetric superresolution imaging', and we hope that this is now better supported by providing 1) additional optical characterisation (including 7 new figures, see yellow boxes), 2) clear illustrations of full MLA illumination, and 3) edits to the main text (see red text) to better conceptually unify the manuscript.
In doing so we hope that we have remedied their concerns.

Reviewer #2 (Remarks to the Author)
The The manuscript is generally well written but could, in my opinion, be considerably sharpened to provide necessary information and additional clarity to the reader.As of now, I feel that some of the comparisons with other methods are not carried out as stringent as I would have liked to see them.Overall, I still consider the manuscript a very valuable addition to the field and I hope that the authors will find the following points useful to improve the manuscript.
We thank the reviewer for their time reading the manuscript and positive response.

Major points
1. Figure 1  We thank the reviewer for this helpful suggestion.We have modified Fig. 1 to now focus on the 3D PSFs and the light field optical implementation specifically.We have also added a new Fig.S2, which details the optical implementations of the other engineered PSFs.We hope that this now also clarifies the difference between the 4f optical configuration and the '3f' optical configuration of SMLFM (where the MLA conducts the phase modification and focuses to an image plane).
2. Figure 1/2: I find it rather confusing to see different pixel sizes for different modalities in, apparently, the same field of views (in terms of constant area?).Is the reason for this a different effective magnification of the optical system?This choice makes comparing achievable emitter densities on a given camera frame area (!) rather difficult.(see also next point).
We thank the reviewer for highlighting this ambiguity and we have expanded the 2. None of the figures of the SI were numbered in the final compiled PDF that I got.(I later saw that the SI itself shows everything correctly) All figure numbers have been checked, with thanks.
3. Figure 1a: unit for density is missing.
We believe the reviewer is referring to Fig. 2a, which has been amended, with thanks.
The simulated FoV is 20 x 20 µm, the figure only shows a 10 x 10 um FoV to enable discernment of PSF shape.
5. line 220-222: phrasing.I somewhat doubt that the division of background photons has a larger effect than adding up the camera noise contributions from adding up seven field of views.Please comment.
Thanks for the comment and to avoid confusion we have edited this sentence as follows: "Therefore, on the basis of speed, SMLFM significantly out-performs the DHPSF at all light levels, particularly at low SNR, due to optical multi-emitter fitting."We have removed 'evanescent wave'.
8. I am surprised to see the mentioning of #1 cover slips.In most cases, the objectives are designed for #1.5 to minimise aberrations etc. Worth checking.
Aberrations were minimised by careful adjustment of the objective correction collar.9. line 575 unit missing.Amended.
10. how "easy" is it to adapt the software/noise model for sCMOS rather than emCCD?
This would be very easy with the only key difference being per-pixel gain.As SMLFM uses existing localisation algorithms this is easily accounted for and compatible with all code implemented in this study.

Reviewer #3 (Remarks to the Author)
Daly et al present a new approach to volumetric SMLM imaging, splitting the light according to its position in the back focal plane and thereby forming multiple images, each taken at a different angle.This is a potentially very useful new approach; while many solutions have been suggested to the challenge of how to discriminate axial position, astigmatism is still the most commonly used method despite its limitations (limited z depth in a single slice, degradation of x or y precision).In particular, the authors demonstrate that their method allows use of substantially higher excitation densities than can typically be used in 3D imaging.Overall this paper represents an important and interesting new technique that could help uncover exciting new biology.However, I have some comments that I would like to be addressed.
We thank the reviewer for their positive comments and recognizing SMLFM as an important technique for uncovering new biology.
While the acquired data is impressive the imaging of B cell receptors have a key limitation.
Given the size of the cell and the number of molecules localised, I estimate that if the molecules are evenly spaced they are around 70 nm apart.They are of course not evenly distributed, but it illustrates that the resolution is likely to be limited in at least some areas by the sampling rather than localisation precision (a common problem when imaging with dSTORM in thick samples).The acquired density of molecules can be limited if only a small amount of the labelled molecule is present, or by the labelling efficiency, the dSTORM blinking degrading, or the acquisition time: the authors should comment on what limited the reconstructed density in this case.
The reviewer's comments regarding sampling rate in the BCR images is greatly appreciated.
To clarify, all dSTORM imaging of B cells was conducted until all blinking events were exhausted and therefore the accumulation of localisations was limited by the abundance of receptors.It is for this reason that we also image highly dense tubulin datasets in HeLa cells.
Here the labelling density is significantly greater, and hence these datasets were used for resolution analysis.
While the BCR imaging might not lead to as high spatial sampling as the tubulin imaging, the rate of localisations over a small detector area illustrates the power of SMLFM at resolving single emitters at high density though optical multi-emitter fitting.Therefore, we believe that combining these two experiments with live-cell tracking covers most scenarios that necessitate high-density volumetric SMLM.
I generally think it is important to benchmark against a known structure in an experiment when presenting new techniques.However in this case, as the focus is on accurate recall at high density rather than resolution per se, I think that the evaluation is satisfactory without additional experiments.
manuscript "High-density volumetric super-resolution microscopy" by Daly et al. focuses on the quantification of accessible emitter densities in single-molecule light field microscopy (SMLFM).In SMLFM, an array of micro lenses (MLA) is placed in the Fourier plane (conjugated back-focal plane) creating a pattern of PSFs that are then recorded via a camera and analysed using standard (for PSF localisation) and custom (for connecting the localisations from the different areas) software.The work is a logical extension of the author's previous work (Sims et al., reference 22), in which the concept and the ability to image an impressive z-range of 8 µm had been demonstrated.Here, the authors used a customised MLA with a hexagonal arrangement improving the usable area on the camera.In addition to the comparison with other methodologies enabling 3D resolution in SMLM, the authors further demonstrate successful single-particle tracking over an extended biological object (B cell receptors).
a/b): If I am not mistaken, the work uses a 4f arrangement of lenses as shown in one of the SI figures and not the arrangement shown here.I would suggest to merge the SI figure and the current Figure 1.